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Factoring quadratic functions

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How do you use the "factor fish" method to factor quadratic exponentials?
Jun 2nd, 2014

Factor –6x2 + 15x + 36

First, I will first remove the common factor of 3, taking the leading negative sign with it:

–6x2 + 15x + 36 = –3(2x2 – 5x – 12)

Then I'll factor the remaining quadratic: 2x2 – 5x – 12 = (x – 4)(2x + 3):

When I write down my answer, I need to remember to include the –3 factor:

–6x2 + 15x + 36 = –3(x – 4)(2x + 3).

A disguised version of this factoring-out-the-negative case is when they give you a backwards quadratic where the squared term is subtracted. For example, if they give you something like 6 + 5x + x2, you would just reverse the quadratic to put it back in the "normal" order, and then factor: 6 + 5x + x2 = x2 + 5x + 6 = (x + 2)(x + 3). You can do this because order doesn't matter in addition. In subtraction, however, order does matter, and you need to be careful with signs.


Jun 2nd, 2014

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